Chapter 27: Wave Optics

(a) As a soap bubble thins it becomes dark, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the bubble can be and appear dark at all visible wavelengths? Assume the same index of redfraction as water.

(b) Discuss the fragility of the film considering the thickness found.

A film of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths? Oil has an index of reddfraction of $1.40$.

Does Huygens’s principle apply to all types of waves?

Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

Repeat Exercise $27.70$, but take the light to be incident at a $45^{{}^{\circ }}$angle.

Repeat Exercise$27.71$, but take the light to be incident at a $45^{\circ }$angle.

Unreasonable Results

To save money on making military aircraft invisible to radar, an inventor decides to coat them with a non-reflective material having an index of refraction of $1.20$, which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers.

(a) What thickness should the coating be to inhibit the reflection of $4.00-\mathrm{c}\mathrm{m}$wavelength radar?

(b) What is unreasonable about this result?

(c) Which assumptions are unreasonable or inconsistent?

What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?

The angle between the axes of two polarizing filters is $45.0^{{}^{\circ }}$. By how much does the second filter reduce the intensity of the light coming through the first?

Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.